The literal rendition of this is of course violence based on prejudice, but in English it is far more common to use the term hate crime. I suppose that the term in Spanish includes violence that does not rise to the level of a crime, or perhaps even a misdemeanor - and so is a broader term. If you wanted to be a stickler and use the less common literal translation I would add a qualifier the first time you use it, something like 'more commonly called hate crimes in English.'
I have been reading about violence against LGBT people in Colombia and in Spanish violencia por prejuicio is widely used to describe it. The report Cuerpos Excluidos, Rostros de Impunidad gives an overview of it. Carlos's is just one rostro of the 110 LGBT people who were killed in Colombia in 2015.